Synthesis of LaCN3, TbCN3, CeCN5, and TbCN5 Polycarbonitrides at Megabar Pressures

Inorganic ternary metal–C–N compounds with covalently bonded C–N anions encompass important classes of solids such as cyanides and carbodiimides, well known at ambient conditions and composed of [CN]− and [CN2]2– anions, as well as the high-pressure formed guanidinates featuring [CN3]5– anion. At still higher pressures, carbon is expected to be 4-fold coordinated by nitrogen atoms, but hitherto, such CN4-built anions are missing. In this study, four polycarbonitride compounds (LaCN3, TbCN3, CeCN5, and TbCN5) are synthesized in laser-heated diamond anvil cells at pressures between 90 and 111 GPa. Synchrotron single-crystal X-ray diffraction (SCXRD) reveals that their crystal structures are built of a previously unobserved anionic single-bonded carbon–nitrogen three-dimensional (3D) framework consisting of CN4 tetrahedra connected via di- or oligo-nitrogen linkers. A crystal-chemical analysis demonstrates that these polycarbonitride compounds have similarities to lanthanide silicon phosphides. Decompression experiments reveal the existence of LaCN3 and CeCN5 compounds over a very large pressure range. Density functional theory (DFT) supports these discoveries and provides further insight into the stability and physical properties of the synthesized compounds.


■ INTRODUCTION
In recent years, advancements in the high-pressure chemistry of nitrides and carbides have unveiled a wealth of surprises.Indeed, at pressures above 50 GPa, many exotic oligo-and polynitrides (i.e. containing N 4 4− , N 6 6− , N 8 6− anions, 1,2 N 6 rings, 3−5 N 18 macrocycle, 6 infinite one-dimensional (1D)polynitrogen chains, 1,7−12 and two-dimensional (2D)-polynitrogen layers 2,12 ) as well as polycarbides (i.e. containing graphene-, polyacene-, and para-poly(indenoindene)-like ribbons 13−16 ) were discovered.Recently discovered binary carbon nitrides C 3 N 4 and CN 2 , built of CN 4 tetrahedra and synthesized at pressures above 70 GPa, 17 possess many remarkable physical properties, such as superhardness, ultraincompressibility, photoluminescence, piezoelectricity, and superconductivity, making these multifunctional materials candidates for technological applications, considering that they are recoverable to ambient conditions.A recent highpressure study of the H−C−N system shows that the addition of another element, namely, hydrogen, helps to produce CN 4 tetrahedra frameworks at lower pressures. 18The addition of metal atoms to carbon nitrides is expected to enable tuning and controlling of the physical properties of such materials.
Therefore, exploration of the ternary metal−C−N systems at high pressures is very promising.
−27 Recently, this family of species was extended with the discovery of the CN 3 5− anion, synthesized at mild pressures (25−54 GPa) and recoverable to ambient conditions. 28,29Knowing that C−N compounds built of CN 4 tetrahedra were obtained at pressures above 70 GPa, 17 as well as the fact that mild pressures (up to 54 GPa) are insufficient for the formation of C−N anions with a tetracoordinated carbon, 29 the stabilization of CN 4 8− units, 30 or/ and the formation of polycarbonitrides built of corner/edgesharing CN 4 tetrahedra in ternary metal−C−N systems are expected at pressures above 70 GPa.The discovery of such compounds might be interesting not only for chemical and materials sciences but also for planetary sciences since these solids can potentially be formed at the boundaries between the rock core and the methane-ammonia-rich mantle of ice-giant planets.
Here we present the high-pressure, high-temperature synthesis and characterization of four hitherto unknown lanthanide polycarbonitrides, LaCN 3 , TbCN 3 , CeCN 5 , and TbCN 5 , at megabar pressures.Their crystal structures were solved and refined based on synchrotron single-crystal X-ray diffraction, unveiling previously unobserved anionic singlebonded carbon−nitrogen three-dimensional (3D) frameworks consisting of CN 4 tetrahedra connected via di-or oligonitrogen linkers.A crystal-chemical analysis demonstrates that polycarbonitride compounds have similarities with lanthanide silicon phosphides.Density functional theory (DFT) calculations cross-validate these discoveries and provide further insight into the stability and physical properties of these compounds.

■ RESULTS AND DISCUSSION
In this study, diamond anvil cells (DACs) were loaded with rare earth metal pieces (La, Tb, and Ce) embedded in molecular nitrogen (N 2 ) or cyanuric triazide (C 3 N 12 ; see the Methods Section for details).The samples were compressed to target pressures between 90 and 111 GPa, and the samples were laser-heated to temperatures reaching 2500 K (Table S1).The resulting multigrain samples, consisting of hundreds of submicron-sized crystallites of the reaction products, were studied by synchrotron single-crystal X-ray diffraction (SCXRD) at the P02.2 beamline of DESY and the ID11, ID15b, and ID27 beamlines of the ESRF.The analysis of the SCXRD data revealed the formation of four metal polycarbonitrides, LaCN 3 , TbCN 3 , CeCN 5 , and TbCN 5 .The refinement against SCXRD data (Figures S1−S4) yields very good agreement factors (see Tables S2−S5 and CIFs for the full crystallographic data).−33 The description of other reaction products, e.g.binary polynitrides, will be discussed elsewhere.
The isostructural LaCN  2) GPa is described below as an example (Figure 1).LaCN 3 consists of four crystallographically distinct atoms: La1, C1, N1, and N2 (see Table S2 and the CIF for the full crystallographic data).Carbon atoms are 4-fold coordinated by nitrogen atoms, forming irregular CN 4 tetrahedra named mirrored sphenoids (Figure 1a).Both N1 and N2 atoms form two single covalent bonds: the N1 atoms form one N1−C1 and one N1−N1 bond between two N1 atoms of different tetrahedra, while the N2 atoms are the common nodes of corner-sharing CN 4 tetrahedra, thus being bonded with two carbon atoms (Figure 1b).4) and 111.6(10)°, respectively.Thus, all nonmetal atoms are sp 3 -hybridized.Lanthanum is 11-fold coordinated by nitrogen atoms.Since all N atoms form two single covalent bonds, each nitrogen atom has a charge of −1 in the fully ionic approximation, in turn implying the expected +3 oxidation state for the La atoms.Carbon, which makes four covalent bonds, is neutral.The bond order analysis for TbCN 3 gives the same charge distribution as for LaCN 3 , suggesting a +3 oxidation state for Tb, one of two well-known oxidation states for this element.The repeating CN 3 3− unit in LaCN 3 and TbCN 3 , as well as its Lewis formula, are presented in Figure S5a,b.
The structure can be described as being built of cornersharing CN 4 tetrahedra chains running along the crystallographic a-axis.These chains are interconnected through the N1−N1 single bonds (Figure 1c).Each chain is linked to four other chains, producing a 3D framework (Figure 1d).Lanthanum atoms are located in the voids of this covalent 3D framework and each surrounded by nine CN 4 tetrahedra.The structure of LaCN 3 has similarities with that of the hightemperature Pnma-KPO 3 phase. 34In the latter, atoms are sitting on the same Wyckoff positions as in LaCN 3 , with the nonmetal atoms forming PO 4 tetrahedra arranged in infinite chains along the crystallographic a-axis through corner-sharing (Figure 1e).However, there are no covalent O−O bonds between the chains, and the distance between these PO 4 corner-sharing chains is larger.
The isostructural compounds CeCN 5 and TbCN 5 crystallize in the monoclinic space group P2 1 /n (#14) with one lanthanide atom (Ce1 or Tb1), one carbon atom (C1), and five nitrogen atoms (N1 through N5) being crystallographically unique and all located on the 4e Wyckoff position (Tables S4 and S5).At a pressure of 90(2) GPa, the lattice parameters of CeCN  When viewed along the a-axis, the structure of CeCN 5 is seen to be composed of large corrugated C 6 N 12 rings.The rings are elongated in a direction close to [011] and arranged in a herringbone pattern (Figure 2c).Each of these C 6 N 12 rings is constituted of six carbon atoms linked through N−N dimers (Figure 2e).There are two distinct dimers within the C 6 N 12 rings, the N2−N2 and the N4−N1 dimers, each with a bond length of 1.449(15) and 1.422(30) Å, respectively, suggesting a single-bond character.Single-bonded N3−N5 dimers (1.419(17) Å) connect the adjacent C 6 N 12 units so that the N3 and N5 atoms are bonded to the C1 and N2 atoms of the C 6 N 12 rings, respectively (Figure 2d,f).Although the N2−N5 bond (1.359(14) Å) is distinctively shorter than other N−N bonds in CeCN 5 , its length is still within the single-bond lengths range. 2,35,36Cerium atoms, located between the layers built of C 6 N 12 rings, are 12-fold coordinated with nitrogen, featuring an average bond length of 2.351(11) Å.
With four of the five nitrogen atoms only making two single bonds, it stands to reason that in the ionic approximation, the repeating CN 5 unit bears a charge of −4, indicative of a +4 oxidation state for Ce, one of its two commonly observed oxidation states.In TbCN 5 , the bond order as well as the hybridization of the C and N is identical to that described in CeCN 5 .Thus, TbCN 5 is composed of the same [CN 5 ] ∞ 4− anion, suggesting a +4 oxidation state for Tb, which is also well known for this element.The repeating CN 5 4− unit in CeCN 5 and TbCN 5 and its Lewis formula are presented in Figure S5c,d.
Similarly to recently discovered high-pressure C 3 N 4 polymorphs, 17 the common building block in LaCN 3 , TbCN 3 , CeCN 5 , and TbCN 5 is the CN 4 tetrahedron.The C−N single-bond lengths and N−C−N bond angles in LaCN 3 , TbCN 3 , CeCN 5 , and TbCN 5 are also similar to those found in the C 3 N 4 polymorphs at similar pressures.While the condensed 3D framework in the C 3 N 4 solids is built exclusively of corner-sharing tetrahedra, the connectivity of these tetrahedra in the polynitrides discovered here is different.The 3D anionic polycarbonitride framework of LaCN 3 and TbCN 3 is built by corner-sharing CN 4 as well as by N−N bonds (Figure 1b).In the CeCN 5 and TbCN 5 structures, the CN 4 tetrahedra do not have common nodes and are linked only by single covalent nitrogen bonds having two types of linkers: dimers and trimers (Figure 2b).
Among the metal−C-N ternary compounds, hitherto exclusively featuring isolated anions (i.e., cyanides, carbodiimides, and guanidinates), the LaCN 3 , TbCN 3 , CeCN 5 , and TbCN 5 solids form a novel unique class of compounds composed of a 3D single-bonded polycarbonitride framework.The geometry of the C−N anions illustrates well how high pressure stabilizes higher coordination numbers of carbon.In the − N�C�N − anion, which is stable under ambient conditions, the C atom is coordinated by two N atoms.At mild pressures (25−54 GPa), the CN 3 5− anion is formed with carbon having a coordination number of three.Here, at higher pressures (90−111 GPa), we observe 4-fold coordinated carbon atoms in the crystal structures of LaCN 3 , TbCN 3 , CeCN 5 , and TbCN 5 .Strikingly, despite the theoretical predictions of the high-pressure stabilized CN 4 8− orthonitridocarbonate anion, 30 we do not observe its formation.This suggests that while CN 4 units are indeed the preferred 3D building blocks, their concatenation is more favorable than preserving significantly negatively charged anions, such as CN 4 8− .According to the ninth high-pressure chemistry rule of thumb formulated in 1998: "Elements behave at high pressures like the elements below them in the periodic table at lower pressures", 37 carbon and nitrogen under high pressure should behave like silicon and phosphorus at lower pressures.Therefore, one can expect similarities between the highpressure LaCN 3 , TbCN 3 , CeCN 5 , and TbCN 5 compounds and the ternary Ln−C−P, Ln−Si−N, and Ln−Si−P solids (Ln represents lanthanide elements) known under ambient conditions.
To get a deeper insight into the stability and physical properties of the novel compounds, DFT calculations were performed using the Vienna Ab initio Simulation Package (VASP) 50 for LaCN 3 and CeCN 5 .Due to the presence of 4f electrons in Ce and Tb, their compounds require higher-level theory.CeCN 5 can be sufficiently well described with the DFT + U method. 51However, it has been shown that Tb is not sufficiently well described by DFT + U 52 and requires higherlevel theory, e.g., DFT + dynamical mean field theory (DMFT). 53The latter is computationally very expensive and requires particular expertise in using it.For this reason, TbCN 3 and TbCN 5 are not investigated through theoretical calculations in this study.The relaxed structure parameters obtained from the variable-cell structure relaxations of LaCN 3 and CeCN 5 compounds closely reproduce the corresponding experimental values (Tables S6 and S7), confirming the validity of our computational methodology.
To trace the structures' behavior at lower pressures and to obtain their equation of state, full variable-cell structure relaxations for the LaCN 3 and CeCN 5 compounds were performed with 10 GPa pressure steps between 0 and 120 GPa (Figure 4).The lattice parameters of LaCN 3 change monotonously in the whole pressure range (Figure S8) and the crystal structure does not undergo any significant changes, indicating the possible recoverability of LaCN 3 to ambient conditions.That is also suggested from phonon calculations: LaCN 3 is dynamically stable both, at the synthesis pressure and at ambient pressure (Figure S6).On the other hand, CeCN 5 is relaxable without structural changes only down to 10 GPa, with its lattice parameters changing monotonously down to that pressure (Figure S9).CeCN 5 is also found to be dynamically stable at its synthesis pressure of 90 and 10 GPa (Figure S7).However, below 10 GPa, full variable-cell structure relaxation resulted in a possible electronic transition in which the 4f electron state is promoted from above the Fermi energy to below (Figure SD1 in Supporting Discussion).It is reminiscent of the promotional model of Zachariasen and Pauling of a γ ↔ α transition in pure Ce, 54−57 though in CeCN 5 the transition occurs upon decompression and leads to a significant modification of the crystal structure of the compound (Figure SD2 in Supporting Discussion).The above observations make CeCN 5 as well as potentially TbCN 3 and TbCN 5 compounds of high interest for investigations of manyelectron effects in these systems at the higher level of the electronic structure theory, e.g., within the DFT + DMFT. 53n accurate theoretical description of the electronic structure and vibrational and structural properties of the compounds with occupied f-states is therefore outside of the scope of the present study.
The volume-pressure dependences of the DFT-relaxed structures of LaCN 3 and CeCN 5 in the pressure range of 0− 120 GPa and 10−120 GPa, respectively, were fitted with a third-order Birch−Murnaghan equation of state (Figure 4).The obtained bulk moduli (K 0 (LaCN 3 ) = 192.5(6)GPa, K 0 (CeCN 5 ) = 250.7(14)GPa) are higher than the bulk moduli of known nitrides and carbides of lanthanum (LaN, 58 La 2 C 3 , 59 LaC 2 59 ) and cerium (CeN, 60 CeC, 59 Ce 2 C 3 , 59 CeC 2 59 ) due to the presence of robust polycarbonitride 3D frameworks with relatively incompressible short C−N and N−N bonds.At the same time, the obtained bulk moduli are lower than the bulk moduli of the ultraincompressible C−N solids, 17 likely because of the dilution of the C−N framework with metal ions.The degree of this dilution is higher in the case of LaCN 3 since the ratio between metal cations and the framework-forming C and N atoms is higher in LaCN 3 than in CeCN 5 , which explains the significant difference in the bulk moduli of LaCN 3 and CeCN 5 .Another reason for the enhancement of K 0 in CeCN 5 compared to the K 0 of LaCN 3 is the smaller size of the Ce 4+ cation compared to that of La 3+ and, as a consequence, shorter and less compressible metal-N bonds.
Considering the dynamical stability at 1 bar and the smooth behavior of the lattice parameters of DFT variable-cell relaxed structures down to ambient pressure, a first attempt to experimentally verify the recoverability of LaCN 3 was undertaken.Upon sample decompression, a data point at 75(2) GPa was successfully collected (Table S8).The unit cell volume of LaCN 3 at 75(2) GPa perfectly matches the DFT-calculated equation of state (Figure 4).However, when the pressure was decreased to 50(2) GPa, the sample chamber collapsed, and it was no longer possible to continue the experiment (see footnote of Table S8).After an unsuccessful decompression experiment, another DAC#4 was prepared and loaded with a lanthanum piece embedded in solid cyanuric triazide (C 3 N 12 ).Cyanuric triazide serves as a precursor of nitrogen (and might be carbon as well) for the synthesis of LaCN 3 as well as a "hard" solid pressure transmission medium.The same P and T conditions were used for the synthesis: the sample was compressed to 101(2) GPa and laser-heated to temperatures reaching up to 2500 K (Table S1).According to synchrotron single-crystal XRD, the LaCN 3 phase was formed (Table S8).Subsequently, DAC#4 was decompressed, and LaCN 3 was preserved in the cell down to 6(2) GPa.Notably, upon the decompression of DAC#4, the unit cell volume of LaCN 3 lay systematically below the DFT-calculated equation of state curve, due to residual stresses in the hard pressure transmitting medium (Figure 4).Below 6(2) GPa, the cell was opened in an Ar glovebox and closed again to avoid an interaction with oxygen and moisture.According to the XRD measurements, LaCN 3 was no longer present.Therefore, LaCN 3 exists at least down to 6(2) GPa, but was not found recoverable under ambient conditions.DAC#2, containing the CeCN 5 compound, was first compressed from 90(2) to 115(2) GPa and then decompressed, allowing data collection from 115(2) to 33(2) GPa.Below that pressure, the sample escaped the experimental chamber, preventing further measurements from being done.In total, seven P−V data points were collected for the CeCN 5 phase, found to persist even down to 33(2) GPa (Table S9).The experimental data agree well with the DFT-calculated equation of state (Figure 4).No decompression experiment was carried out for DAC#3, containing the TbCN 3 and TbCN 5 compounds.
The computed electron densities of states for LaCN 3 and CeCN 5 at the synthesis pressure and at low pressure are shown in Figure 5. LaCN 3 has band gaps of 2.2 and 1.7 eV at 102 GPa and 1 atm, respectively.CeCN 5 has a gap between the valence and conduction bands that is 3.2 eV at the synthesis pressure.Between the valence and conduction bands lie the unoccupied Ce 4f states.The gap from the valence band to the edge of the 4f band is 1 eV, and the 4f peak has a width of 1.4 eV.Upon decompression to 10 GPa, the band gap between the valence and conduction band decreases to 2.7 eV.The gap from the valence band to the 4f band edge is 0.6 eV, and the 4f peak has a width of 1.1 eV.The exact position of the unoccupied 4f peak is influenced by the choice of the U value.A higher value of U shifts the peak away from the Fermi energy.A larger value of U also slightly decreases the gap between the valence and conduction band.A similar effect of shifting the 4f peak and decreasing the band gap has also been observed in studies on CeO 2 . 51Both LaCN 3 and CeCN 5 compounds demonstrate a pressure-induced band gap opening.

■ CONCLUSIONS
In this study, the four compounds LaCN 3 , TbCN 3 , CeCN 5 , and TbCN 5 (first representatives of the class of polycarbonitrides) were synthesized in laser-heated diamond anvil cells at pressures between 90(2) and 111(2) GPa.Their crystal structures are built of a covalently single-bonded carbon− nitrogen anionic 3D framework consisting of CN 4 tetrahedra connected via di-or oligo-nitrogen linkers.From a crystal chemistry perspective, the closest ambient condition analogues of these polycarbonitrides are Ln−Si−P metal silicon phosphide ternary compounds.
According to DFT calculations, the CeCN 5 phase is dynamically stable down to 10 GPa and not stable under ambient conditions, while LaCN 3 is (meta)stable under ambient conditions.While experiments did not validate the recoverability of the LaCN 3 solid, one can expect that other high-pressure metal polycarbonitrides built of CN 4 connected only by vertexes or partially N−N connected can be recoverable, analogously to the high-pressure C 3 N 4 polymorphs, and CN 2 compound containing N−N bonds.LaCN 3 and CeCN 5 are found to be semiconductors with a pressuremediated band gap opening.
Due to the presence of hard polycarbonitride 3D frameworks with relatively incompressible short C−N and N−N bonds, LaCN 3 and CeCN 5 exhibit good mechanical properties with the bulk moduli higher than the bulk moduli of known nitrides or carbides of lanthanum and cerium.At the same time, the bulk moduli of lanthanide polycarbonitrides are lower than the bulk moduli of the ultraincompressible C−N solids, 17 and dictated by the degree of dilution of the C−N framework with metal ions having longer and more compressible Ln−N contacts.
■ METHODS Sample Preparation.BX90-type DACs 61 equipped with Boehler-Almax type diamonds 62 of 120 μm (DAC#1, DAC#2, DAC#4) and 80 μm (DAC#3) culet diameter were used in these experiments.The sample chambers were formed by preindenting rhenium gaskets, initially 200 μm in thickness, down to 15−18 μm and laser-drilling a hole of 60 μm (DAC#1, DAC#2, DAC#4) or of 40 μm (DAC#3) in diameter in the center of the indentation.Pieces of lanthanide metals (La, Ce, Tb, 99.9%, Sigma-Aldrich) were placed in the sample chamber of individual DACs (DAC#1, DAC#2, DAC#3) directly in contact with one of the two diamond anvils, and molecular nitrogen was then loaded using high-pressure gas loading systems at the Bayerisch Geoinstitut (BGI, 1300 bar) 63 or at the Centre for Science at Extreme Conditions (CSEC, 2000 bar).The Ce metal was loaded into the DAC in an Ar-filled glovebox, while La and Tb were loaded in air.DAC#4 was loaded with a lanthanum piece and solid cyanuric triazide (C 3 N 12 ), and the lanthanum piece was placed in contact with one of the two diamond anvils.Caution: Since the energetic cyanuric triazide compound is to some extent unstable against external stimuli, proper safety precautions should be taken especially when handling the materials in amounts exceeding those that are typically used for an experiment in a DAC.Laboratory personnel should wear protective equipment like grounded shoes, leather coats, Kevlar gloves, ear protection, and face shields.The samples were compressed to their target pressure (Table S1) and laser-heated (λ = 1064 nm) up to 2500(500) K using a homemade laser-heating system at BGI 64 or in CSEC.The temperatures reached during laser heating were determined by fitting the sample's thermal emission spectrum to the gray body approximation of Planck's radiation function in a given wavelength range (570−830 nm).The pressure in the DACs was determined using the Raman signal from the diamond anvils 65 and additionally monitored by the X-ray diffraction signal of the Re gasket edge using rhenium's equation of state. 66X-ray Diffraction.The X-ray diffraction studies were conducted at the P02.2 beamline of Petra III, DESY (λ = 0.2904 Å); the ID11 beamline (λ = 0.2846 Å), the ID15b beamline (λ = 0.4099 Å), and the ID27 beamline (λ = 0.3738 Å) of the Extreme Brilliant Source European Synchrotron Radiation Facility (EBS-ESRF).At the P02.2 beamline of DESY, the X-ray beam was focused down to 2 × 2 μm 2 and data was collected with a PerkinElmer 1621 XRD flat-panel detector.At the ID11 beamline of the ESRF, the X-ray beam was focused down to 0.75 × 0.75 μm 2 and data was collected with an Eiger2X CdTe 4 M hybrid photon counting pixel detector.At the ID15b beamline of ESRF, the X-ray beam was focused down to 1.5 × 1.5 μm 2 and data was collected with an Eiger2X CdTe 9 M hybrid photon counting pixel detector.At the ID27 beamline of the ESRF, the X-ray beam was focused down to 2 × 2 μm 2 and data was collected with an Eiger2X CdTe 9 M hybrid photon counting pixel detector.In order to determine on which sample position the SCXRD data should be collected, a full X-ray diffraction mapping of the pressure chamber was performed.The sample position displaying the most and the strongest single-crystal reflections belonging to the phase of interest was chosen for the collection of single-crystal data, collected in step scans of 0.5°from −36 to +36°.The CrysAlis Pro software package 67 was used for the analysis of the SCXRD data (peak hunting, indexing, data integration, frame scaling, and absorption correction).To calibrate the instrument model in the CrysAlis Pro software, i.e., the sample-to-detector distance, detector's origin, offsets of the goniometer angles, and inclination of both the X-ray beam and detector with regard to the instrument axis, a single crystal of orthoenstatite [(Mg 1.93 Fe 0.06 )(Si 1.93 ,Al 0.06 )O 6 , Pbca space group, a = 8.8117(2) Å, b = 5.18320(10) Å, and c = 18.2391(3)Å] was used.The DAFi program was used for the search of groups of reflections belonging to individual single-crystal domains. 68With the OLEX2 software package, 69 structures were solved with the ShelXT structure solution program 70 using intrinsic phasing and refined with the ShelXL 71 refinement package with the least-squares minimization.Crystal structure visualization was made with the VESTA software. 72heoretical Calculations.Calculations were carried out by the Vienna Ab initio simulation package (VASP), 50 using the projector augmented wave (PAW) method. 73Table S10 contains information about the used POTCARs.For LaCN 3 , the GGA-PBE functional was used in standard DFT formalism. 74For CeCN 5 , due to the presence of localized 4f electrons, the L(S)DA + U formalism as formulated by Dudarev et al. was employed to account for the on-site Coulomb repulsion. 75The label (S) in L(S)DA + U, was omitted for simplicity.In the Dudarev et al. formalism, the LDA + U functional takes the form where ρ is the density matrix of 4f states, and U and J are the spherically averaged matrix elements of the screened Coulomb electron−electron interaction. 75Only the difference between U and J is significant, and thus, U − J is simply denoted as U.For CeCN 5 , a U = 6 eV was used.The value of U was chosen based on a semiempirical approach to agree with the experimental values of the lattice constants.4][55][56][57]76 For both LaCN 3 and CeCN 5 compounds, spin-polarized calculations were employed to account for possible local magnetic moments. Caculations for structure relaxations and eDOS were done for the LaCN 3 and CeCN 5 compounds with a 6 × 6 × 6 k-point mesh according to the Monkhorst−Pack method.77 For the relaxations, a Gaussian smearing was used with a smearing of 0.03 eV.For eDOS calculations, the tetrahedron method of Blochl was used.78 The convergence criteria for the energy were set to 10 −7 eV, and in structure relaxations, the forces on each ion were less than 10 −3 eV/Å.These settings were used for both LaCN 3 and CeCN 5 .The plane-wave cutoffs were set to 680 eV for LaCN 3 and 740 eV for CeCN 5 .Phonons were calculated with the finite displacement method, with displacements generated by phonopy.79,80 For both LaCN 3 and CeCN 5 , 2 × 2 × 2 supercells were 3 and TbCN 3 solids crystallize in orthorhombic space group Pnma (#62).The lattice parameters of LaCN 3 are a = 4.1059(12) Å, b = 4.870(5) Å, and c = 7.4758(15) Å at 102(2) GPa, while those of TbCN 3 are a = 3.9813(15) Å, b = 4.7305(12) Å, and c = 7.2358(15) Å at 111(2) GPa.The crystal structure of LaCN 3 at 102(

Figure 1 .
Figure 1.Crystal structure of LaCN 3 at 102(2) GPa and that of the high-temperature phase of Pnma-KPO 3 at ambient pressure.LaCN 3 : (a) Representation of the main building block�the CN 4 tetrahedron.(b) Connectivity of the CN 4 tetrahedra.Values of bond lengths obtained from the experiment are shown in black, while those obtained from the DFT calculations are shown in red.(c, d) Views along the crystallographic b-and a-axes.La atoms are shown as green spheres, C atoms as yellow spheres, and all N atoms (both N1 and N2) as blue spheres; the thin black lines outline the unit cell.(e) Crystal structure of Pnma-KPO 3 at 1 atm 34 viewed along the crystallographic b-axis.K atoms are shown as purple spheres, P atoms as gray spheres, and O atoms as red spheres; the thin black lines outline the unit cell.

Figure 2 .
Figure 2. Crystal structure of CeCN 5 at 90(2) GPa.(a) Representation of the main building block�the CN 4 tetrahedron.(b) Connectivity of the CN 4 tetrahedra.Values of bond lengths obtained from the experiment are shown in black, while those obtained from the DFT calculations are shown in red.(c, d) Crystal structure of CeCN 5 viewed along the crystallographic a-and b-axes.The full red line in (c) helps visualize the atoms constituting the C 6 N 12 rings, highlighted in (d) by a red dashed line.The thin black lines outline the unit cell.(e) Depiction of the carbonitride network's C 6 N 12 ring, when viewed along the crystallographic a-axis.(f) Two adjacent C 6 N 12 rings interconnected through N5−N3 dimers, viewed along the crystallographic b-axis.Cerium, carbon, and nitrogen atoms are represented as light green, yellow, and blue spheres, respectively.

Figure 3 .
Figure 3. Anionic frameworks of the pairs of compounds with similar connectivity of tetrahedra: (a) LaCN 3 /TbCN 3 and (b) Cmc2 1 -LaSi 2 P 6 , both built of the 3D framework of corner-sharing CN 4 or SiP 4 tetrahedra connected via N−N or P−P linkers; (c) CeCN 5 /TbCN 5 and (d) I-42d-Eu 2 SiP 4 consisting of CN 4 or SiP 4 tetrahedra linked exclusively via N−N or P−P bonds, producing a 3D framework.The C, N, Si, and P atoms are shown as yellow, blue, light brown, and gray balls, respectively.The thin black lines outline the unit cell.

Figure 4 .
Figure 4. Pressure dependence of the unit cell volume of LaCN 3 and CeCN 5 .The black symbols represent calculated data points obtained from DFT, and the red and blue symbols represent experimental data points obtained from SCXRD data.The black and blue lines are fits of the DFT data with a third-order Birch−Murnaghan equation of state.The parameters of the fit for LaCN 3 are V 0 = 198.19(4)Å 3 , K 0 = 192.5(6)GPa, and K p = 4.214(12), while for CeCN 5 , they are V 0 = 239.98(9)Å 3 , K 0 = 250.7(14)GPa, and K p = 4.14(3).